2. • An exact divisor of a number is known as its .
E.g.- 1, 2, 4, 8 are factors of 8.
• 1 is the factor of every number.
• Also every number is a factor of itself.
• It should be less than or equal to the given number.
• There are finite numbers of factors for any number.
• The product of two numbers is known as their .
• Every number is a multiple of 1 and itself.
• There are finite number of multiples.
• All the multiples of 2 are known as even numbers and
those which are not are known as odd number.
• A number having 1 and itself as its factor is known as
. E.g.- 2, 3, 5, 7, 11 etc.
• A number having more than two factors is known as
.
• 1 is neither prime nor composite.

3. • Divisibility of numbers by 2
Numbers with 0, 2, 4, 6, 8 in their one’s/unit’s place are
divisible by 2.
• Divisibility of numbers by 3
A number is divisible by 3 if the sum of all of its numbers is
divisible by 3.
• Divisibility of numbers by 4
A number is divisible by 4 if the last two digits i.e., is divisible
by 4.
• Divisibility of numbers by 5
Numbers with 0, 5 in their one’s/unit’s place are divisible
with 5.
General rule of divisibility:
If a number is divisible by other number then it is also divisible
by the factors of the other number.
E.g.- 81 is divisible by 9, and 3 is factor of 9, so 81 is also
divisible by 9. 81/3 = 27

4. • Representing a number as the product of its prime factors is
known as .
E.g.- 100 = 2 x 5 x 2 x 5
• The greatest of all the factors of the given numbers is known
as their
. E.g.- H.C.F. of 18 and 36 is 18
18 = 2 x 3 x 3
36 = 2 x 2 x 3 x 3
G.C.D. = 2 x 3 x 3 = 18
• The smallest of all the multiples of the given numbers is
known as their . E.g.- L.C.M.
of 10 and 15 is 30
10 = 5 x 2
15 = 3 x 5
L.C.M. = 5 x 3 x 2 = 30
• If the common factor of two numbers is only 1 then the
numbers are called .
• All the numbers are the factors of 0.

5. To find the H.C.F. and L.C.M. of the given numbers we always
need not do prime factorization.
• Finding H.C.F. of the given numbers by division method:
Step 1 – Divide the highest of the given number with the next
highest number given.
Step 2 – If the remainder is 0 then the divisor is the H.C.F. of the
two numbers, then divide it with the next highest number, if again
the remainder is 0 then divide the divisor with next number and so
on. If the remainder is not 0, then, divide the divisor with this
remainder, repeat the chain of divisions until the remainder is 0,
the divisor with which we got remainder 0 is the H.C.F. of the given
numbers.
• Finding L.C.M. of the given numbers by division method:
Step 1 – Write the given numbers in a row.
Step 2 – Divide the numbers with the smallest prime number
which divides one or more of the given numbers.
Step 3 – Write the non divisible numbers as they are, in the next
row and continue this division till the row has all 1s.

6. Q1. Sort the following
numbers as even and odd:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Click here for answer.
Q2. Find the H.C.F. &
L.C.M. of 6, 9, 15, 30.
Click here for answer.
Q3. Test divisibility of
the following
numbers by 5:
216, 215, 199, 9090.
Click here for
answer.
Q4. Prime factorize
the following:
35, 99, 166, 343.
Click here for
answer.